An Application of STWS Technique in Solving Stiff Non-linear System: 'High Irradiance Responses' (HIRES) of Photomorphogenesis

This paper illustrates an application of the Single Term Walsh Series (STWS) technique in solving stiff non-linear system: ‘High Irradiance RESponses’ (HIRES) of Photomorphogenesis from plant physiology. The chemical reaction scheme of HIRES problem has been modelled into system of stiff non-linear differential equations. This stiff system has been solved using the STWS technique. The STWS solutions are compared with the results obtained by the well-known solvers, namely, VODE and RADAU5. The applicability of the STWS technique has been tested

Comparison of Single Term Walsh Series Technique and Extended RK Methods Based on Variety of Means to Solve Stiff Non-linear Systems

This paper presents a comparison of Single Term Walsh Series (STWS) technique and the extended Runge-Kutta (RK) methods based on variety of means such as Arithmetic Mean (AM), Harmonic Mean (HaM), Centroidal Mean (CeM) and Contraharmonic Mean (CoM) to solve stiff non-linear systems of initial value problems (IVPs). Numerical solutions of some stiff non-linear systems are investigated for their stiffness. The discrete solutions obtained through STWS technique are compared with that of the RK methods based on variety of means. The applicability of the STWS technique has been demonstrated. The results show that the STWS technique is more suitable to solve stiff non-linear systems including highly stiff problems

The GREAT-ER model as a tool for chemical risk assessment and management for Chinese river catchments

The Chinese government has introduced a range of policies with the aim to improve freshwater quality to safe levels for both humans and ecosystem function. These policies form an important part of sustainable economic development. An important component of the improvement in surface water quality is to assess and reduce the risk from organic chemicals. The development of reliable predictive tools is therefore required which can be used for the purpose of chemical risk assessment and catchment management. The catchment scale Geo-referenced Regional Exposure Assessment Tool for European Rivers (GREAT-ER) model was developed for this purpose. Its application in China would represent a valuable water quality management tool. However, the data requirements for the parameterization of GREAT-ER are difficult to meet, especially in countries with limited data accessibility such as China. A methodology has been developed to facilitate the use of the GREAT-ER model in any catchment in China. Key methodological contributions include an approach to locate sewage treatment works (STW), estimate population served and to estimate the distribution and magnitude of untreated emissions. Low-flow statistics were estimated by means of regional regression. The GREAT-ER model was applied to the East river catchment for the chemicals Triclosan (TCS), Triclocarban (TCC), Estrone (E1) and 17β-estradiol (E2). As part of the study, a sampling campaign was conducted in January 2016 to collect water samples from sites within the East river catchment; samples were subsequently analysed to determine the concentration of target chemicals. These data, along with data obtained from collaborators collected in December 2008, were used to estimate the accuracy of the model. Overall, the model performed well for E1 and E2. However, there were some significant errors in the model’s estimation for the concentration of TCC and TCS. This included a number of remote rural subcatchments, which may be a reflection of the affordability of personal care products to the rural population. These, and other factors, were explored during validation of the model. A risk assessment was performed for the four chemicals for the years 2016 and 2020. In 2016, the model estimated that TCC would not exceed the predicted no effect concentration (PNEC) anywhere in the catchment, however, in 2020 the PNEC was exceeded for 3 stretches, each downstream of major STWs. The model estimated that the concentrations of E1 and E2 in 2016 would exceed PNEC values in stretches largely confined to the heavily urbanised Shenzhen catchment, but also isolated minor stretches located downstream of population centres. In 2020, the number of stretches exceeding the PNEC threshold reduced for areas with improved wastewater treatment infrastructure, but overall, the area that exceeded the PNEC for E1 and E2 was estimated to expand. TCS posed a high risk to the catchment in 2016, with the model predicting the PNEC to be exceeded throughout much of the catchment. In 2020, it was estimated that the same stretches would exceed the PNEC for TCS, but concentrations would be considerably higher overall. A series of catchment management scenarios were then utilised, such as increasing STW removal efficiency and the expansion of STW connectivity. These infrastructure developments were found to be effective for E1 and E2, but not so for TCS

The Theory of Functional Connections: A Journey from Theory to Application

The Theory of Functional Connections (TFC) is a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The functionals derived from this method, called "constrained expressions," analytically satisfy the imposed constraints and can be leveraged to transform constrained optimization problems to unconstrained ones. By simplifying the optimization problem, this technique has been shown to produce a numerical scheme that is faster, more accurate, and robust to poor initialization. The content of this dissertation details the complete development of the Theory of Functional Connections. First, the seminal paper on the Theory of Functional Connections is discussed and motivates the discovery of a more general formulation of the constrained expressions. Leveraging this formulation, a rigorous structure of the constrained expression is produced with associated mathematical definitions, claims, and proofs. Furthermore, the second part of this dissertation explains how this technique can be used to solve ordinary differential equations providing a wide variety of examples compared to the state-of-the-art. The final part of this work focuses on unitizing the techniques and algorithms produced in the prior sections to explore the feasibility of using the Theory of Functional Connections to solve real-time optimal control problems, namely optimal landing problems

Sleep Stage Classification: A Deep Learning Approach

Sleep occupies significant part of human life. The diagnoses of sleep related disorders are of great importance. To record specific physical and electrical activities of the brain and body, a multi-parameter test, called polysomnography (PSG), is normally used. The visual process of sleep stage classification is time consuming, subjective and costly. To improve the accuracy and efficiency of the sleep stage classification, automatic classification algorithms were developed. In this research work, we focused on pre-processing (filtering boundaries and de-noising algorithms) and classification steps of automatic sleep stage classification. The main motivation for this work was to develop a pre-processing and classification framework to clean the input EEG signal without manipulating the original data thus enhancing the learning stage of deep learning classifiers. For pre-processing EEG signals, a lossless adaptive artefact removal method was proposed. Rather than other works that used artificial noise, we used real EEG data contaminated with EOG and EMG for evaluating the proposed method. The proposed adaptive algorithm led to a significant enhancement in the overall classification accuracy. In the classification area, we evaluated the performance of the most common sleep stage classifiers using a comprehensive set of features extracted from PSG signals. Considering the challenges and limitations of conventional methods, we proposed two deep learning-based methods for classification of sleep stages based on Stacked Sparse AutoEncoder (SSAE) and Convolutional Neural Network (CNN). The proposed methods performed more efficiently by eliminating the need for conventional feature selection and feature extraction steps respectively. Moreover, although our systems were trained with lower number of samples compared to the similar studies, they were able to achieve state of art accuracy and higher overall sensitivity